New Developments in the Numerical Conformal Bootstrap

Abstract

The numerical conformal bootstrap has become in the last 15 years an indispensable tool for studying strongly coupled CFTs in various dimensions. Here we review the main developments in the field in the last 5 years, since the appearance of the previous comprehensive review \cite{Poland:2018epd}. We describe developments in the software ({\tt SDPB 2.0}, {\tt scalar\_blocks}, {\tt blocks\_3d}, {\tt autoboot}, {\tt hyperion}, {\tt simpleboot}), and on the algorithmic side (Delauney triangulation, cutting surface, tiptop, navigator function, skydive). We also describe the main physics applications which were obtained using the new technology.

49 pages, 11 figures. Version to appear in Rev.Mod.Phys. Typos fixed

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Cited by in corpus (22)

• Bootstrapping the 3d Ising Stress Tensor
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Exploring Confinement in Anti-de Sitter Space
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Bootstrapping the Quantum Hall problem
• Conformal Fields from Neural Networks
• The tricritical Ising CFT and conformal bootstrap
• The thermal bootstrap for the critical O(N) model
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Bipartite Fluctuations of Critical Fermi Surfaces
• Analytic trajectory bootstrap for matrix models
• 1d Conformal Field Theory and Dispersion Relations
• Correlators in phase-ordering from Schrödinger-invariance
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• Sparsity in the numerical six-point bootstrap
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• A Fuzzy Sphere Journey in Critical Phenomena
• Bootstrapping SU(3) Lattice Yang-Mills Theory
• Exact 3D Conformal Blocks from Fractional Calculus
• Bootstrapping periodic quantum systems